LpLq Off-diagonal estimates for the Ornstein-Uhlenbeck semigroup

Some positive and negative results

Journal article (2017)

Authors

Alex Amenta Analysis - EEMCS
J.J.B. Teuwen ImPhys/Optics - AS , Netherlands Cancer Institute
Research Group
Analysis (EEMCS) (TU Delft)
Ornstein-Uhlenbeck semigroup Mehler kernel Off-diagonal estimates
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Published Date

2017

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

We investigate Lp(γ)-Lq(γ) off-diagonal estimates for the Ornstein-Uhlenbeck semigroup (etL)t>0. For sufficiently large t (quantified in terms of p and q), these estimates hold in an unrestricted sense, while, for sufficiently small t, they fail when restricted to maximal admissible balls and sufficiently small annuli. Our counterexample uses Mehler kernel estimates.